Integral of e^(-2x)/(e^-x + 1) (substitution)

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🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:13 Substitution: u=e^-x
00:19 Differentiate in both sides
00:33 Substitute e^-x and (e^-x)dx
00:50 Rewrite expression
01:07 Split into two integrals
01:26 Simplify expression and integrate 1 and 1/(u+1)
01:41 Undo substitution: u in terms of x
01:52 Add integration constant +C
02:00 Final answer!
02:05 See more!

𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭𝐬
► Integration by parts: 🧑‍🔧 Integration by parts
► Integration by substitution: 🧑‍🔧 Integration by substitution
► Integration by trig substitution: 🧑‍🔧 Integration by trig substitution
► Integration by Weierstrass substitution: 🧑‍🔧 Integration by Weierstrass substi...
► Integration by partial fraction decomposition: 🧑‍🔧 Integration by partial fraction d...

🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐨𝐟 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐬𝐨𝐫𝐭𝐞𝐝 𝐛𝐲 𝐥𝐞𝐯𝐞𝐥 (𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡) 𝐢𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮.𝐜𝐨𝐦:
► Integration by parts 👉 https://integralsforyou.com/integrati...
► Integration by substitution 👉 https://integralsforyou.com/integrati...
► Integration by trig substitution 👉 https://integralsforyou.com/integrati...
► Integration by Weierstrass substitution 👉 https://integralsforyou.com/integrati...
► Integration by partial fraction decomposition 👉 https://integralsforyou.com/integrati...

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